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Show linear vector space using matrix-vector multiplication. y = AC = [a1 a2 a3...an] * [c1 c2 c3 .... cn]. [c1 c2 c3 .... cn] is in column form
Category Archives: Matrix and Signal Processing
Vector Space S = { y varepsilon R^m | y = Ac, c varepsilon R^n }
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Vector Space S = { y varepsilon R^m | y = Ac, c varepsilon R^n }
What is the dimension of S?
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What is the dimension of S?
Can we say that the number of independent directions that the space S spans to be the dimension of S?
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Can we say that the number of independent directions that the space S spans to be the dimension of S?
What is the dimension of the universe that we live in?
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What is the dimension of the universe that we live in?
is dim(S) = n?
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is dim(S) = n?
What is the dimension of a plane?
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What is the dimension of a plane?
If we take one more vector orthogonal to the plane, then what will be the dimension?
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If we take one more vector orthogonal to the plane, then what will be the dimension?
Define/describe Linear vector space in terms of the vectors [a_1, a_2, …., a_n]
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Define/describe Linear vector space in terms of the vectors [a_1, a_2, ...., a_n]
In the above case, if x and y are vectors in S, Does x + y belong to S?
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In the above case, if x and y are vectors in S, Does x + y belong to S?
In the above case, if x is a vector in S, does cx belong to S? c is in R
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In the above case, if x is a vector in S, does cx belong to S? c is in R
Give more rigorous mathematical notation of Linear Vector Space.
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Give more rigorous mathematical notation of Linear Vector Space.
What is the notation to represent a vector of real numbers or real-complex numbers?
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What is the notation to represent a vector of real numbers or real-complex numbers?
Upper case bold letter — matrix or scalar or vector?
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Upper case bold letter -- matrix or scalar or vector?
Upper case non-bold letter — matrix or scalar or vector?
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Upper case non-bold letter -- matrix or scalar or vector?
Is a vector usually a column vector? what is the ith column in a Matrix A? $a_i$ what does it mean? $a_j^T$ what does it mean? How is the $j^th$ element represented?
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Is a vector usually a column vector? what is the ith column in a Matrix A? $a_i$ what does it mean? $a_j^T$ what does it mean? How is the $j^th$ element represented?
What do you mean by the concept of vector space?
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What do you mean by the concept of vector space?
What are bases?
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What are bases?
What do you mean by Linear Vector Spaces?
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What do you mean by Linear Vector Spaces?
If S is a linear vector space, what are the properties of S?
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If S is a linear vector space, what are the properties of S?
What do you mean by matrix dimensions?
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What do you mean by matrix dimensions?
Can you represent a matrix of real numbers with m * n dimensions with notations?
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Can you represent a matrix of real numbers with m * n dimensions with notations?
Can you represent a matrix of complex numbers with m * n dimensions with notations?
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Can you represent a matrix of complex numbers with m * n dimensions with notations?
What is the outcome of matrix multiplications? is the multiplication outcome a number?
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What is the outcome of matrix multiplications? is the multiplication outcome a number?
What are tall matrices? What are short matrices?
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What are tall matrices? What are short matrices?
What is a square matrix?
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What is a square matrix?
What is a diagonal matrix?
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What is a diagonal matrix?
What does dimension mean for a single vector?
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What does dimension mean for a single vector?
What are the various interpretations of matrix multiplication operations?
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What are the various interpretations of matrix multiplication operations?
What are matrix determinants?
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What are matrix determinants?
What is the significance of matrix determinants?
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What is the significance of matrix determinants?
What is linear dependence?
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What is linear dependence?
What is a subspace?
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What is a subspace?
What are the related ideas of subspace?
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What are the related ideas of subspace?
What is a row space?
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What is a row space?
What is a column space?
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What is a column space?
What is the rank of a matrix?
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What is the rank of a matrix?
What is a vector norm?
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What is a vector norm?
What are the different types of Matrix multiplication?
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What are the different types of Matrix multiplication?
What is the Big Block perspective of Matrix Multiplication?
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What is the Big Block perspective of Matrix Multiplication?
Do the multiplication approaches apply to the big block cases? and/or vice versa.
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Do the multiplication approaches apply to the big block cases? and/or vice versa.
What is linear independence?
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What is linear independence?
Give some examples of Auto-Regressive Processes?
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Give some examples of Auto-Regressive Processes?
What is the relation between Auto-Regressive Process and Toeplitz systems?
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What is the relation between Auto-Regressive Process and Toeplitz systems?
Can we say that voice and video signals, sinewaves-plus-noise, signals in control systems and signals induced by earthquakes are some examples of Auto-Regressive Processes?
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Can we say that voice and video signals, sinewaves-plus-noise, signals in control systems and signals induced by earthquakes are some examples of Auto-Regressive Processes?
What is Levinson Durbin Recursion?
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What is Levinson Durbin Recursion?
Difference: Auto-Regressive and Auto Correlation.
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Difference: Auto-Regressive and Auto Correlation.
What is a lattice filter structure?
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What is a lattice filter structure?
Can you utilize the structure of a Toeplitz matrix to find solutions that have lower algorithmic (flops, operation count) complexity?
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Can you utilize the structure of a Toeplitz matrix to find solutions that have lower algorithmic (flops, operation count) complexity?
What is adaptive filtering?
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What is adaptive filtering?
What is an AR system?
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What is an AR system?
What do the covariance matrices of Stationary signals look?
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What do the covariance matrices of Stationary signals look?
Can you solve Toeplitz systems using Gaussian elimination?
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Can you solve Toeplitz systems using Gaussian elimination?
How does a Toeplitz Matrix relate to Stationary or non-stationary signals?
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How does a Toeplitz Matrix relate to Stationary or non-stationary signals?
What is Gaussian elimination?
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What is Gaussian elimination?
Can you solve Toeplitz systems using Cholesky Methods?
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Can you solve Toeplitz systems using Cholesky Methods?
If you solve Toeplitz systems using Gaussian Eliminations, what is the algorithmic complexity (algorithm)?
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If you solve Toeplitz systems using Gaussian Eliminations, what is the algorithmic complexity (algorithm)?
Define Cholesky Methods?
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Define Cholesky Methods?
What is a Toeplitz Matrix?
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What is a Toeplitz Matrix?
Will in a Toeplitz Matrix, the elements parallel to the diagonal be the same? If so, how?
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Will in a Toeplitz Matrix, the elements parallel to the diagonal be the same? If so, how?
What is a Toeplitz Matrix?
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What is a Toeplitz Matrix?
Will in a Toeplitz Matrix, all elements in a diagonal be the same? If so, how i.e. give examples?
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Will in a Toeplitz Matrix, all elements in a diagonal be the same? If so, how i.e. give examples?
Give examples?
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Give examples?
What is regularization?
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What is regularization?
What is LMS algorithm? Linear Mean Square.
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What is LMS algorithm? Linear Mean Square.
What is the role of QR decomposition in LS analysis?
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What is the role of QR decomposition in LS analysis?
What is QR decomposition?
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What is QR decomposition?
PLS and Machine Learning. How are they related?
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PLS and Machine Learning. How are they related?
What is PLS? Partial Least Square?
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What is PLS? Partial Least Square?
What is principle component analysis?
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What is principle component analysis?
What is Linear Least Square?
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What is Linear Least Square?
What are Generalized Eigenvalues?
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What are Generalized Eigenvalues?
What is an Ordinary LS?
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What is an Ordinary LS?
Give examples of Linear Least Square?
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Give examples of Linear Least Square?
What are pseudoinverses?
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What are pseudoinverses?
What is whitening?
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What is whitening?
What is a Quadratic Form?
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What is a Quadratic Form?
What is Gaussian Elimination?
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What is Gaussian Elimination?
Derive the Gaussian Eliminataion?
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Derive the Gaussian Eliminataion?
Give an example of Gaussian Elimination?
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Give an example of Gaussian Elimination?
Give an example of SVD.
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Give an example of SVD.
What is SVD? i.e. What is Singular Value Decomposition?
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What is SVD? i.e. What is Singular Value Decomposition?
Show an example of an Eigen decomposition?
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Show an example of an Eigen decomposition?
What are the pros and cons of Eigen Decomposition?
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What are the pros and cons of Eigen Decomposition?
What is Eigen Decomposition?
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What is Eigen Decomposition?
What is an Eigenvalue?
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What is an Eigenvalue?
What is a Matrix Space?
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What is a Matrix Space?
What are row spaces and column spaces?
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What are row spaces and column spaces?
What is a Vector Space?
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What is a Vector Space?
What is a Matrix Space? Give an Example.
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What is a Matrix Space? Give an Example.
